Li, Bingren et Yang, Yimin, On extending real functions to finite dimensional algebras, Acta mathematica Sinica. English series (Print) , 15(4), 1999, pp. 455-470
In a finite dimensional real algebra, we define functional calculus for real functions. The analytic hypothesis is replaced by a differentiable hypothesis. High order differentibility is essentially necessary and sufficient to our discussions. Moreover, we give some examples.